Chapter  details my first paper in this area, "Style Transfer by Relaxed Optimal Transport and Self-Similarity" or STROTSS [1]}. This work leverages two key ideas which my future work builds upon. The first of these is that the distribution of localized features is too complex to be modelled with simple summary statistics, the same philosophy that lead to patch-driven approaches to texture synthesis. The distinctive textural elements of a style can be modeled far better by explicitly matching local style features to local content features using non-parametric tools such as optimal transport or nearest neighbors. In this work we propose a 'style loss' that measures the distance between two empirical distributions of features using an approximation of the Earth Mover's Distance (EMD). The second key idea is that human perception is extremely robust, and improvements in style transfer's visual quality can be achieved by relaxing definitions of 'content' to take advantage or these robust dimensions of perception. In this work we were inspired by pareidolia (see Figure REF ), and propose a content loss based on self-similarity that is invariant to global translations and orthonormal affine transformations of feature space. Together these novel definitions of 'content' and 'style' lead to outputs that not only better match the target style, but also better preserve content by reducing artifacts. Via a large user study we demonstrate that the proposed method offerd a pareto-dominant tradeoff between stylization and content preservation relative to prior work.
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